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Unformatted text preview: Math 115–Test 1 Sample Problems September 2009 Name To receive credit you must show all your work. 1. Let f ( x ) = x- x 2 . (a) Find the slope of the line tangent to the graph of f at the point x = a by using the definition of the derivative. (b) Using your results from part (a), find an equation of the line tangent to the graph at x = 2 . 2. Let f ( x ) = 1 /x . When simplified, the difference quotient f ( x + h )- f ( x ) h becomes (A) 1 x ( x + h ) (B) 1 x ( h- x ) (C)- 1 x 2 (D) 1 x ( x- h ) (E)- 1 x ( x + h ) 3. Consider the graph of f(x) shown to the right. x y 1 2 ! 1 ! 2 ! 3 ! 4 1 2 3 ! 1 3 f(x) (a) lim x → (- 1)- f ( x ) = (b) lim x →- 1 f ( x ) = (c) lim x → 2 f ( x ) = (d) f (2) = (e) f (1) = (f) lim x → 2 + f ( x ) = (f) f ( x ) is NOT continuous at x = (g) f ( x ) is NOT differentiable at x = 4. The mathematics office sells sample midterms for 50 cents each. The cost of producing x tests (in cents) is given by C ( x ) = 1000- 60 x + x 2 . (a) Find the equations for the revenue function R ( x ) and profit function P ( x ) ....
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